Wednesday, December 30, 2020

Defamation Law vs Censorship

Mac Isaac, the laptop repairman with whom Hunter Biden apparently left a laptop, has sued Twitter. His complaint is not that Twitter locked the New York Post account of the contents of the laptop's hard drive. It is that their explanation for locking it was the claim that the account was in violation of Twitter's hacked material rules, and that Twitter, in explaining that policy, defines a hack as

an intrusion or access of a computer, network, or electronic device that was unauthorized or exceeded authorized access.

By Isaac's account of what happened, his access to a laptop that had been dropped off at his shop for repair and then abandoned was authorized, hence not a hack. It followed that Twitter was making false statements which, according to Isaac, have had large negative effects on him. On the face of it, it looks like a legitimate case.

What made the story of particular interest to me was that Isaac is doing something I had thought about doing, decided not to do, and suggested to a law firm that they might do in similar cases — with regard to Facebook, not Twitter. 

About a year ago, I discovered that Facebook was blocking all links to my web page. Anyone who attempted to put up such a link got a message saying that the page violated Facebook's community standards. I went through the procedures on Facebook to object, never got any response. Eventually they stopped blocking it, still with no explanation.

Facebook is a private firm, and as such has a legal right to decide what messages they will or will not publish. They do not have a legal right to defame me, which, assuming that nothing on my page actually violated their community standards, they were doing. The problem had been solved when they stopped blocking the page, and in any case was never a large enough problem to justify the trouble of a court case. But it occurred to me that it might justify a class action by someone else, so I emailed a law firm that seemed appropriate with the suggestion.

Mac Isaac, or his attorney, apparently had the same idea in a much larger case, and has now acted on it. I wish him well.

Sunday, December 13, 2020

How to Waste Vaccine

The CDC estimates that, as of the end of September, there had been 53 million Covid infections in the U.S., 7.7 times the number of reported cases. The current figure is 16.2 million cases, so if the ratio holds, total number of infections is about 125 million. That is probably too high, since the ratio of infections to cases goes down as the amount of testing goes up, so I will guess a current figure of 100 million.

The U.S. has contracted for enough vaccine from the two sources that have been or almost certainly will be approved to vaccinate another 100 million over the next few months. Combine those numbers and we should have 200 million people who either have had the disease and so are very nearly immune or have been vaccinated and so are very nearly immune, getting us at least close to the level required for herd immunity. Add in the number who will have gotten the infection by then and we should probably be over that level, which means the number of infections should start falling.

There is one problem with this optimistic story. As best I can tell from online discussions, the current plan for allocating the vaccine does not include any attempt to avoid giving it to people who have already had the disease, not even to those who have been diagnosed with it. If so, about a third of the first hundred million doses will be wasted on people who don't need them.

One possible argument for doing it that way is that having Covid does not create perfect immunity, there having been a few cases reported of someone who got the disease, recovered, and was later reinfected. But the vaccine does not create perfect immunity either — reported effectiveness for the first two is about 95%. If as many as five percent of those who had had the disease and recovered were still vulnerable to it, we should have had a lot more than a few cases of reinfections.

To make that argument more precise, consider that, as of the end of September, there had been about seven million reported cases. If infection gave only 95% immunity, about 350,000 of them should have still been vulnerable, a little more than one thousandth of the population. Since the end of September there have been another nine million cases, so more than nine thousand of them should have been known reinfections, individuals who were diagnosed with the disease, recovered, and were then diagnosed again. That did not happen. It follows that, while infection may not give complete immunity, it gives considerably better immunity than the vaccines.

Another possible argument is that tests for whether someone has already had the disease have a significant false positive rate. Checking online, it looks as though the false positive rate for most such tests is below ten percent (specificity>.9). At ten percent, that means that if you skip the people who test positive you are vaccinating an additional ten people for every false positive you are not vaccinating, which sounds like a substantial positive. If we had enough vaccine for everybody it might be better for everyone to get vaccinated, but we don't.

If my analysis is correct, current policy is lethally stupid. 

People who know more about this than I do are invited to correct either my interpretation of what is currently being done or my argument for what ought to be.

Friday, December 04, 2020

Why Not Add Gluten?

I'm currently on a low glycemic index diet, following advice from Bredesen's book The End of Alzheimer's. So far as I know I don't have Alzheimer's, but I do have one copy of the genetic variant that makes it more likely and I have observed what I think is age-related cognitive decline, most notably the fact that I can no longer easily memorize poems. Given the theory behind Bredesen's book, I think his approach has a reasonable chance of helping even if the cause is normal aging rather than Alzheimer's.

Being on such a diet raises an interesting set of problems — how to replace high glycemic foods I like, which include wheat, rice, potatoes, and things made from them such as bread and pasta, with low glycemic substitutes. I have found some solutions to that, including a southern Indian pancake made from mung bean flour, which we happened to have some of, that works for enchilada-like dishes, crepe wrapped around a filling. Also barley as a substitute for rice, barley being apparently the one grain with a really low glycemic index.

The challenge is bread. Looking around the web, I find multiple recipes using almond flour or coconut flour. But, as some of the recipes concede and my limited experience confirms, the result is not very much like a wheat bread. To quote one such recipe: 

When making this paleo and keto almond flour bread, it is important to adjust our expectations. The yeasty aroma and gluten-induced fluffiness that we love about traditional bread cannot be achieved without yeast and gluten.

So this is more of a quick bread that fills the need (if you still have it) to make a sandwich or to have a slice of bread for breakfast.

This raises an obvious question. Almond flour or coconut flour or mung bean flour doesn't have gluten. Wheat flour does. Why not add some of the gluten from wheat flour to one of the other flours and then make an ordinary raised bread, using yeast or sourdough?

One reason is that some people are, or at least believe they are, allergic to gluten — the webbed recipes routinely describe the bread as low-carb and gluten-free, and obviously regard the latter as a plus. I am not, to the best of my knowledge, allergic to gluten. Gluten has some carbohydrate as well as a good deal of protein, so adding it probably raises the glycemic index of bread, but as best I can tell it should only take about ten percent of the flour being straight gluten to produce something that will rise like wheat flour, which shouldn't raise it by much. 

My one experiment along these lines so far, an attempt at a sourdough bread made mostly from mung bean flour, was a flop, with an off taste that neither I nor other members of my family were willing to eat, but it doesn't follow that there is no way of doing it. Almond flour seems to be the preferred ingredient for the quick breads that I have found recipes for, so I may get some of that and continue my experiments, probably using yeast instead of sourdough.

The question is, why isn't this already being done — or is it? There are a lot of people out there who are diabetic or near-diabetic and are looking for low carb/low glycemic index foods. There are a lot of foods out there advertised as fitting that requirement. Are there raised yeast breads made from one of the nut or bean based flours with added gluten? If not, is the reason that it isn't doable, in which case I am wasting my time trying to make one?

Anyone know?

Wednesday, December 02, 2020

The Audiobook of my novel Salamander is Out

I have a bunch of promo codes, which can be used to get a free copy in exchange for agreeing that, if you like it, you will post a favorable review somewhere, most likely although not necessarily on Amazon. If you want one, email me for it. 

So far as I can tell, Audible is providing me promo codes for the U.S. but not for the U.K., which may mean that the ones for the U.K. went to Robert Power, who narrated the book. If you are in the U.K. and want one I can forward your request to him.

My email is

I also have promo codes, U.S. and U.K., for the audio versions of The Machinery of Freedom and Future Imperfect, both narrated by me.

Friday, November 27, 2020

The Real Scandal Behind Qualified Immunity

Police officers attack someone, beat him up, arrest him with a false claim that he assaulted them or resisted arrest. Unfortunately for them, someone recorded the action on his cell phone. Eventually charges are dropped and the victim sues. The police officers defend themselves under the doctrine of qualified immunity, the legal rule that holds that they are not civilly liable unless their act was not only illegal but obviously illegal, sometimes interpreted as requiring a past case where the same act was found illegal by a court. 

The defense sometimes fails, often succeeds, a result that has gotten quite a lot of criticism, much of it probably deserved. What mostly doesn't get criticized is the fact that actions which are, on their face, obviously criminal — beating someone up is assault and battery, whether or not the perpetrator is a police officer — are being punished, if at all, only by a civil suit. 

The reason is quite simple. Legally speaking, the victim of the crime is not the person who was beaten up, it is the state he lives in. If Mr. Smith assaults me and the case comes to trial, it will be not Friedman vs Smith but State of California vs Smith. Criminal prosecution is controlled by the state, so crimes the state does not want to prosecute don't get prosecuted. If Mr. Smith happens to be a police officer, the state knows that prosecuting him, convicting him, and locking him up for a year will make it harder to hire police officers, as well as provoking conflict with the police union. So, most of the time, it doesn't. A civil case is created and controlled by the actual victim, so in practice civil cases are usually the only way of punishing criminal acts by people the state approves of, such as its employees.

This issue was first brought to my attention in a case where the crime in question was not assault and battery but first degree murder, the killing of two Black Panthers by Chicago police back when I was a graduate student in Chicago. None of the killers were tried, but the city, state, and county ended up settling civil claims for well over a million dollars. 

There is a possible solution, one that actually existed in a legal system ancestral to ours. In England in the 18th century, any Englishman could prosecute any crime. In one famous case, a magistrate instructed troops to open fire on a crowd of demonstrators, several people were killed, and the magistrate ended up tried for murder. 

If he had been convicted the King could have pardoned him, but pardoning an official, or a policeman, who has been convicted of murder is a much more visible act than never charging him. And England in the 18th century still had in law, although not in practice, a legal action, the Appeal of Felony, which was an entirely private suit for a criminal penalty. The King was not a party to the suit and so, according to Blackstone, could not pardon a convicted defendant.

For more on the subject, see the chapter on 18th Century England in my Legal Systems Very Different from Ours. A late draft is webbed.

Covid: Cases vs Deaths

News stories keep reporting record numbers of cases but not record numbers of deaths. Santa Clara County, where I live, shows detailed information on both, and the divergence is striking: Looking at the graphs, the case rate began to climb rapidly about a month ago, the death rate appears to be holding roughly steady. We would expect deaths to lag cases, but not by a month.

The divergence is less striking in the U.S. figures, but it's still there. Roughly speaking, over a period when case rates are more than tripling, death rates are doubling. I don't have the data in a form that would let me do a more precise comparison, but that seems to be the pattern so far.

Three possible explanations occur to me. One is that we have more testing, with the result that more of the milder cases are being spotted. If so, the reported increase in cases exaggerates the real change. A second is that we have gotten better at treating Covid, which would be good news but consistent with the increase in cases being real. A third is that fewer of the patients are old. Has anyone here spotted an analysis of the data that can distinguish among those alternatives? 

Thursday, November 26, 2020

Two Sections of my Next Book Up For Comments

As I have mentioned here before, I am currently mining fifteen years of blog posts for one or more books. I now have drafts  of the first two sections of one book webbed for comments, a section on libertarianism and a much shorter section on religion. Feel free to comment here or by email to

Saturday, November 21, 2020

Evidence that Aging Can Be Reversed

There is a recent report out on an Israeli experiment which seems to have reversed two of the cellular processes associated with aging — shortening of telomeres and cellular senescence. It used hyperbaric oxygen, given daily over a period of months, and the effects appear to be large.

It's possible that the result will turn out to be mistaken — the confidence intervals for the various effects include zero, although most of them are significantly positive. It is also possible that the experiment is changing the cellular markers and not whatever underlying biology they are associated with.

The obvious next things to do are to repeat the experiment, ideally with more subjects and varying the procedure, and to observe the subjects of the first experiment to see whether physical effects of aging are being reduced.

But if it's real, it's huge, since the experimental results are for humans, not mice, the procedure should be easy to duplicate at relatively low cost, and we ought to have much clearer results in only a few more years. I've been saying for a long time that the cure for aging will probably come in time for my children but not for me, but perhaps I was wrong.

I would be interested in comments from anyone here with relevant expertise.

Thursday, November 19, 2020

Is the governor of California a Liar or a Hypocrite?

Gavin Newsom, who has supported a variety of restrictions in order to slow the spread of Covid, was caught blatantly violating his own rules, attending a dinner with a large number of unrelated people, sitting close together, not wearing masks. He claimed it was outdoors, but that turned out to mean a room that had glass doors to the outside which were closed because the dinner party was a noisy one. He has been suitably apologetic, conceded that it was something he ought not to have done.

There are two possible interpretations of his behavior, depending on whether one regards the primary function of masks as protecting the wearer or protecting everyone else. If it is protecting the wearer, than his behavior is strong evidence that he doesn't believe in the claim on which his rules are based, since he was willing to do without that protection for himself. At least, he doesn't believe in it for men in their late fifties — and there has been no suggestion in the rules he imposed that they only apply to those of us sixty-five and over.

If one believes, perhaps more plausibly, that the primary function is protecting other people, than his behavior is evidence that he is a hypocrite, willing to impose on other people risks that he forbids them from imposing on each other, but not that he does not believe the claim those rules are based on.

A third possibility is that he is merely a snob, someone who believes in his heart, although he would never say, that pandemic diseases only infect his social inferiors.

Thursday, November 12, 2020

What I Find Depressing About the Election Outcome

From a short term standpoint, the outcome was about as good as I could reasonably hope for, assuming that the Republicans will win at least one of the two Georgia Senate runoffs. I was mostly worried that one party, more probably the Democrats, would end up with control of both houses and the White House. Since I expect either party to do mostly bad things, divided government is the least bad alternative.

In the longer run, the situation is depressing. Trump did well enough so that, whether or not he tries to run again, the coalition he created will survive. That means that we will have, for the foreseeable future, two parties neither of which has even a rhetorical commitment to the free market. The Republicans are against free trade and immigration, and the Democrats are against practically everything else.

Wednesday, November 11, 2020

Did the FDA Deliberately Help Biden Win?

 If so, do you approve?

The FDA and Pfizer arranged to have the tests that ended up showing their vaccine more than 90% effective done last Wednesday, the day after the election. It's clear from the account of what happened that there were multiple decisions that could have been made a little differently and would have produced the information a little sooner.

The obvious conjecture is that the timing was deliberate, that they expected a positive result and thought that announcing it before the election would help Trump. The alternative is that this is just another example of the FDA being (I think over) cautious, making absolutely certain the vaccine works, at a cost of about a thousand lives for every day of delay.

The more interesting question, for me, is whether Biden supporters believe that if it did happen, they approve. Would such a decision count as indefensibly using powers given to the FDA for entirely different purposes to meddle in the election, or as a responsible decision to save America from another four years of Trump? How deeply is "The end does/doesn't justify the means" embedded in the value system of commenters here and on FB, where I also posted a version of this?

Also of interest is whether there are any Trump supporters who believe that, if it happened, it was a defensible, if unfortunate, decision, that they would approve if something similar had been done by someone on their side.

You can find my view of the ends/means question in the relevant chapter at:…/Ideas%20I_%20A%20Book%20fro…

That's a collection of draft chapters for the book I'm currently writing.

Saturday, November 07, 2020

Designing Trump Mark Two

Trump lost this time, but it's clear that, politically speaking, he was doing something right as well as some things wrong, pulled into his coalition quite a lot of new people while pushing other people out. Suppose another politician wanted to copy the successful parts of his strategy while avoiding, so far as possible, the unsuccessful parts. How would he do it?

Part of what worked was coming across as someone who could not be pushed around, who responded to attacks by counter attacking. Would it work to tone that down a little, only attack people who are very clearly attacking him rather than anyone who says anything critical? Or would that just lose him opportunities to show what a he-man he is?

I suspect that the rhetorical exaggeration, the sort of thing that comes across to many as deliberate lying — "we'll build a wall and make Mexico pay for it" — also helped him with his supporters, not because they believed him but because they automatically discount that sort of bluster and the discounted version was something they could believe in. 

The Mark Two version would have to keep Trump's major positions, including hostility to immigration and trade, unfortunate from my point of view but pretty clearly part of what worked. It didn't cost him the Hispanic vote, as many seem to have expected — he did better there than any Republican candidate since Eisenhower. I'm not sure if he has to maintain Trump's policy of outsourcing judicial choice to the Federalist Society, one of the two features of his term that I on the whole approved of. He has to be willing to appoint judges conservatives will like, but that isn't necessarily the same thing. He probably does have to maintain Trump's hostility to foreign military intervention, the other thing I approved of — unless there is some incident such as 9/11 that makes a hawkish response briefly popular with almost everyone. 

One thing I'm not sure of is how much, if any, of Trump's crude, rude, abrasive presentation produces a net gain in votes, how much a net loss.

I haven't been distinguishing between what the candidate has to do to get elected, which Trump did, and what he has to do to get re-elected, which pretty clearly at this point Trump is not doing. And these are preliminary thoughts. Do others have ideas? I am more or less assuming that Trump Mark Two would be another Republican, but he might not have to be.

Friday, November 06, 2020

What the Polls Got Most Wrong

I've just been reading a very perceptive piece by Andrew Sullivan, a left of center writer generally skeptical of left-wing orthodoxy. One part of it struck me as especially interesting:

Eric Kaufmann, one of the most astute political scientists writing today, notes that the segment of the Trump vote the polling missed was educated white voters. He suspects they were afraid to say out loud to pollsters how they were really going to vote. After all, “45% of Republicans with degrees, compared to 23% of Democrats with degrees, said they feared that their careers could be at risk if their views became known.”

So the polling got the less inhibited white non-college-educated Trump voters right, but the graduates very wrong: “The exit polls show that Trump ran even among white college graduates 49-49, and even had an edge among white female graduates of 50-49! This puts pre-election surveys out by a whopping 26-31 points among white graduates.” The threat of wokeness both alienated educated white voters — and caused more of them to vote Trump than anyone expected. The problem with woke media is that they mislead Democrats who then misread the country.

Another part of the Sullivan post that I liked:

And this is where I think I have been wrong about Trump’s appeal, and where I think I’ve misunderstood why otherwise decent people could support such a foul disrupter of democratic norms. Many of them simply didn’t take Trump’s threat to our system seriously. They took all his assaults on democracy as so much bluster from the kind of car salesman he is. They deal with this kind of bullshit all the time, took liberal democracy for granted and saw little reason to fret about its future. The writer Jamie Kirchick says that everything Trump says makes sense if it is preceded by the following words: “And now, Donnie from Queens, you’re on the air.” Many people heard Trump exactly that way, and couldn’t see what all the fuss was about.

The one thing I think Sullivan, along with a good many people I'm seeing on FB, gets wrong, is concluding that the fact Trump has apparently lost says something important about the American people. Trump losing has important implications for the next four years. But in an election this close, where the result would have been reversed if one percent of the votes switched from Biden to Trump,  which side of the win line the outcome came out on says very little about the electorate.

Sullivan provides parts of his output free by email, which is how I am getting it, a larger amount, along with reader comments, for subscribers on Substack. I considered subscribing, as a substitute for Slate Star Codex until it reappears, possibly also on Substack. But unlike SSC, Sullivan's The Weekly Dish posts only a selection of reader's comments, and I don't feel entirely comfortable participating in a conversation where whether my comments appear is up to someone else. 

But I may change my mind. Certainly this post was worth reading. 

Thursday, November 05, 2020

Capitalist vs Socialist

 I had a debate today with Richard Wolff, a socialist economist, and it has been webbed.

Wednesday, November 04, 2020

Two Scenarios for Future Fiction

I have been thinking about ways in which things might develop over the next few decades and have two ideas that someone might build stories around.

1. Permanent Covid. Suppose it turns out that a vaccine producing long term immunity is not possible and that even short term is not very reliable or comes with unacceptable risks, so society has to adapt to the continued existence of the disease, as it already has to flu. Mortality rates will presumably go down as we get better at treating the disease but remain substantial for the more vulnerable parts of the population, especially the old. What happens?

One is that retiring at something between 65 and 75 becomes social as well as professional. Younger people, facing a mortality risk of under one chance in a thousand, mostly ignore Covid, as they mostly ignore flu now. Older people interact almost entirely with each other. With luck, we have either fast and cheap testing or some subset of people known to be immune, so there can be some younger people interacting with the older, but for the most part, medical care for the elderly is provided by elderly nurses and physicians, haircuts by elderly barbers. Interaction with adult children and grandchildren is either online, as I currently Skype with my grandson every week, or carefully organized with suitable precautions, perhaps as one weekend a month in some suitably isolated holiday spot, with everybody getting tested immediately before the event starts.

After a decade or so, it's the new normal.

2. The Unplanned Results of Vote by Mail. One feature of mail-in voting that I have not seen discussed is that it makes vote buying possible. For a mass production version, the purchaser buys hundreds of ballots, fills them in, has them signed in a variety of handwritings — nobody is actually likely to check, even if the signature is supposed to match one on file somewhere — and mails them in. 

The obvious place to start is with local elections where fifty or a hundred votes can change the outcome. But once you have a hundred ballots, selling only the votes on one issue is an obvious waste; you may not care about everything else on the ballot, but other people do and will pay for their desired results. Buying votes will presumably remain illegal, but with a reasonably well organized black market, such as what existed for alcohol under prohibition or for other illegal drugs since, it might be doable. As with bootlegging, it could become a recognized, if not openly approved of, part of the system. As the market develops, probably online and protected by public key encryption, it looks more and more like a conventional market, with known prices for what are, after all commodities — one vote for candidate X is a perfect substitute for another. 

My wife, reading this over my shoulder, objects that vote buying, unlike bootlegging, is not a victimless crime. The candidate you are buying votes against has an incentive to go after the seller — who is, after all, breaking the law. I am not so sure. After all, that candidate may also want to buy some votes, in this election or the next. If he has a reputation as a trouble maker who tries to get honest businessmen into trouble with the law, he may have a hard time finding a seller.

Friday, October 30, 2020

If Trump Loses, What Happens to the Republican Party

It seems likely, although not certain, that Trump will lose the election. If so, what happens to the Republican party? I can see four possible alternatives:

1. Trump remains in control, the party remains as the populist coalition he created. 

2. Trump gives up control, deliberately or otherwise, but the party remains as his coalition, under new leadership.

3. The party reverts to more or less what it was before Trump. Most of the blue collar voters he attracted return to the Democratic party, many of the traditional Republicans who he lost come back. 

4. The party reforms itself as a different coalition. Having lost many of the voters attracted by Trump, it needs to find support somewhere else. The obvious source is the center, Democrats unhappy with the extreme progressive policies that Biden at least says he will follow and that the young Turks of the Democratic Party, led by AOC, will push, liberals repelled by the very unliberal approach of the Woke faction.

This is the most interesting possibility, especially for libertarians, since we might find ourselves included in such a coalition.

P.S. (November 4th A.M.) It is now clear that if Trump loses, as he probably but not certainly will, it will be in a very close election. Also that he has been surprisingly successful in shifting minority voters, especially Latinos but apparently blacks as well, towards the Republican party. 

I conclude that either option 1 or 2 will almost certainly hold for the next four years.

Thursday, October 29, 2020

The Puzzle of Hell Solved

One  problem for Christians is how to make belief in Hell, eternal torture for sinners, consistent with belief in a benevolent and all powerful God. A possible solution is to deny that Christian doctrine requires the existence of Hell. Observing an argument over that question, one  based on interpretations of the text of scripture, it occurred to me that there is a simple solution to the problem of making scriptural references to Hell consistent with a benevolent God, a solution that should be obvious to an economist if not to a theologian.


The belief in Hell is useful as an incentive not to sin. Once a sinner has died, torturing him serves no useful purpose, so there is no reason for a benevolent God to go through with it. If it is still possible for the sinner to reform and be saved he should be given another chance, as portrayed by C.S. Lewis in The Great Divorce. If he is a hopeless case, he can be painlessly removed from existence.


The obvious explanation of the available evidence, the explanation consistent with both the text and divine benevolence, is that scriptural references to Hell are a strategic lie. I do not know if there is evidence in scripture that God sometimes lies, but I do not see how there could be evidence that he never does.

Wednesday, October 21, 2020

Mortality from the Herd Immunity Strategy, a BOTE Estimate: Second Try

I have now redone my calculations, using the CDC data that a commenter on my previous post pointed me at. The results are less optimistic. [Some further revisions have now been included]

Recently, three epidemiologists came out with a public statement arguing for a policy of reaching herd immunity by protecting old people from Covid while letting it spread through the younger population. The proposal has been supported by some, fiercely criticized by others. I have not seen any calculation of what the costs of such a policy would be, so I decided to do one.

My Model

Everyone seventy or over is quarantined, kept from contact with anyone who might carry the virus. The virus is permitted to spread through the rest of the population, controlled only to the extent of not overloading the hospital system. Since this is a simple model, I assume we do it perfectly. The result is an infection rate that just fills available hospital beds, kept down to that if necessary by the sorts of restrictions we are familiar with. Eventually the unquarantined population reaches herd immunity, meaning that each infected person passes the infection to no more than one other person, at which point the number of infected persons starts to decline. When it gets low enough so that we can end quarantine without producing a significant number of deaths, we do so. All of my calculations are for the U.S.

The Numbers

My main source is the CDC’s COVID-19 Pandemic Planning Scenarios. Where figures are given for different age groups, I try to estimate the average for under 70’s.


Ratio of infections to case counts: 11

Median days of hospitalization for those not admitted to the ICU:3.5

Median days of hospitalization for those admitted to the ICU: 12

Percentage of those hospitalized admitted to the ICU: 30%

Infection Fatality Ratio under 70: .0015

Infection Fatality Ratio 70+ .054


Early calculations assumed, implausibly, that everyone was equally likely to catch the disease, and concluded that herd immunity required about 80% immune. Dropping that assumption lowers the number, since as the more at risk people get infected, die, or recover, the average vulnerability of the population falls. By how much it lowers it is not known. In my calculations I assume that 60% does it. That is the point at which the disease just reproduces itself. As more people get infected and either die or become immune, the number infected starts to go down.

The second problem is that, while we have reasonable estimates of how many people die, we do not know how many have been infected, since many infections are not detected. I am using the estimate of 11 from the CDC, but they report a range of possible values from 6 to 24.


These numbers let me calculate mortality from the model:

Cases so far: 8.35 million

Infections so far: 8.35x11=92 million

U.S. population: 328 million

Required for herd immunity: 197 million

Additional infections required: 197 million – 92 million = 105 million

Resulting mortality: 105 million x .0015 = 158,000

This is not the total mortality resulting from my model, since herd immunity is only the point at which, without precautions, infections stop increasing.

Suppose we want to maintain quarantine until we reach the point where dropping it will result in no more than ten Covid deaths/week. If N is the number of infected individuals at that point and Ro is 2, meaning that if nobody was immune or taking special precautions, each person would pass on Covid to 2 others over a contagious period of about two weeks, then the number who get Covid in the next week will be N x (fraction of the population not immune) =N[.09 (the people just leaving quarantine)x236/328 (fraction of them not immune)] +N/total population = .065N +N/328,000,000. The number who die will be that times the infection mortality rate for people 70+, since at this point most of the under 70’s will be immune. Ignoring the second term, which is tiny, we have .054x.065N = .0035N =10. So N = 10/.0035 = 2900. 

So if we maintain quarantine until there are only 2900 cases, dropping quarantine will result in about ten deaths a week from Covid.

Timing Calculations

How long does the process take before it is safe to end quarantine?

Numbers from various online sources:

Total staffed hospital beds: 924,000  

ICU beds, "medical surgical" or "other ICU" (not counting neonatal ICU, burn care, etc.): 63,000

I assume that half of the beds can be used for Covid patients.

Percent of cases requiring medical care: 20%

From the CDC figures, 14% go to regular beds for an average of 3.5 days.

6% go to the ICU and have an average hospital stay of 12 days.

The CDC page does not say how much of that time is in the ICU, but I found another source that reported a median length of stay in the ICU, for studies outside of China, of 7 days. That source gave a median for total hospital stay outside of China of 5 days, which is higher than the CDC figure, so I take its ICU length of stay figure as a high estimate and use it. That implies that cases that go to the ICU consume 7 days of ICU care plus 5 days of ordinary care.


It follows that each case consumes, on average, .42 days of ICU care and .79 days of regular care. So 462,000 regular beds can handle 585,000 cases a day but 31,500 ICU beds can only handle 75,000 cases a day, making the ICU beds the bottleneck. The number of infections is 11 times the number of cases, so the hospital system can handle the result of 825,000 infections a day.


The herd immunity figure I have been using so far is for the whole population, including those in quarantine. About 9% of the population are 70 or over, so the not-quarantined population is 91%. They reach herd immunity with 96 million infections. At the maximum the ICU beds can handle, that takes 116 days or about 17 weeks. At that point the number of infections starts to decline and the ICU beds are no longer at capacity.


The hospitals are handling 5.775 million infections/week, or about 1.9% of the not-quarantined population. Using a spreadsheet, I calculated that by week 43, the number of infections would be down to 2900. At that point 44% of the non-quarantined population have been infected, so total mortality is .0015 x .44 x 298,000,000 = 196,000.


The current death rate from Covid is about 750/day. Suppose we assume that mass vaccination sufficient to reduce that to near zero will occur in six months, which seems if anything a bit pessimistic. At the current death rate, that results in about 135,000 deaths. Since I am assuming mass vaccination by week 26, I ought to cut off my model at that point as well. That drops the number infected to 43%, reducing mortality to 192,000.It follows that if the numbers in my model are correct, we are probably better off not following the model, at least as judged by number of deaths.

What Might Change the Conclusion?

If my model and my assumptions are correct we are better off not following the model, at least measured by mortality. Many of the assumptions are uncertain, however, and the difference between the results of the two strategies is not all that large, which raises the question of whether there are plausible changes in either the model or the parameters that would reverse that conclusion.

Tweaking the Model

One possibility would be to include in the quarantine people under seventy who were for one reason or another at unusually high risk, thus bringing down the mortality rate for those not in the quarantine.

What Might Change the Conclusion?

The mortality figures are not very sensitive to the assumptions that went into my calculation of how long the process would take, although the timing is. The three parameters that could substantially alter the result are the ratio of infections to cases, the mortality rate estimates, and the requirement for herd immunity.

The CDC gives ranges for the first two. At the high end of the range for the ratio of infections to costs, we are almost at herd immunity already, so the mortality costs of the model would be much less. At the low end of the mortality rate estimates, total mortality is about half as great, reversing the conclusion. The same would be true of any substantial reduction in the requirement for herd immunity.

The conclusion is also, of course, sensitive to the assumptions about the alternative to the model. If death rates rise significantly or if mass vaccination takes longer than I assume, that might raise the mortality from the present strategy above that of the model.

As should be obvious, my conclusions are uncertain, both because I am working with a simplified model and because many of the relevant parameters are uncertain. And I am ignoring lots of practical issues associated with mass quarantines. But a back-of-the-envelope calculation is still better than nothing.

Commenters are invited to try to duplicate my calculations and see if I have made any mistakes — I have found and corrected several in the past day.

Tuesday, October 20, 2020

My Brief Talk About My Father

I was recently asked to record something for the ceremony inducting my father, and a number of other people, into the New Jersey Hall of Fame. The whole ceremony is now webbed. My talk starts at 1:04:19. Some here may find it of interest.

Sunday, October 18, 2020

The Cost of Getting to Herd Immunity: A Back of the Envelope Calculation

Recently, three epidemiologists came out with a public statement arguing for a policy of reaching herd immunity by protecting old people from Covid while letting it spread through the younger population. The proposal has been supported by some, fiercely criticized by others. I have not seen any calculation of what the costs, in lives and money, of such a policy would be, so I decided to do one.


The numbers are very uncertain, for at least two reasons. One is that we do not know what percentage of the population must be immune to reach herd immunity. Early calculations assumed, implausibly, that everyone was equally likely to catch the disease, and concluded that herd immunity required about 80% immune. Dropping that assumption lowers the number, since as the more at risk people get infected, die, or recover, the average vulnerability of the population falls. By how much it lowers it is not known. In my calculations I assume that 60% does it. 

The second problem is that, while we have reasonable estimates of how many people die, we do not know how many have been infected, since many infections are asymptomatic and not detected. I am using infection mortality calculations by John Ioannidis along with an estimate from the CDC a while back that the number infected in the U.S. is about ten times the number of known cases. The two are roughly consistent, at least for Santa Clara Country where I live, which happens to provide quite detailed information on mortality. Using those assumptions, and assuming a policy that protects everyone 70 or over, I get:

7.7 million known cases so far, implying 77 million infections which is 23% of a population of 331 million

Required to reach herd immunity, an additional 37% or 122 million infections

Infection mortality rate for people under 70, Ionidas data for Santa Clara County, .07%.

.0007x122 million = 85,000 deaths.

The mortality figures assume adequate hospital space, so the next question is how long the process would take if done at a rate that does not overload the hospitals. To calculate that, I use the following numbers , based on a web search:

Total staffed hospital beds: 924,000 

ICU beds, "medical surgical" or "other ICU" (I'm not counting neonatal ICU, burn care, etc.): 63,000

 The following are much rougher numbers, also based on webbed information.

Time in hospital, non-ICU, two weeks

Time in hospital, ICU cases, 1 week ICU + 1 week non-ICU

Since I am assuming that only a tenth of infections show up as known cases, 122 million infections imply 12 million cases. According to webbed information, 20% of cases end up requiring hospital care, of which 42% go to the ICU. From my assumptions, I get:

2.4 million hospitalized, of which 1 million are in the ICU. So total non-ICU load is 3.8 million non-ICU patient weeks, 1 million ICU patient weeks. If we assume that half of both sorts of beds are being used for non-Covid patients, that implies that we could provide the non-ICU beds in a little over 8 weeks, but that the ICU beds would take 32 weeks. We should allow about another six months (guesswork — I haven't done calculations) for the infection rate to get low enough so it's safe to end quarantine.

[Correction: This assumes that the ratio of hospitalization to infections is independent of age. If we instead assume that it changes with age in proportion to mortality, that lowers my hospitalization figures by about a factor of three, so time until herd immunity is only about 11 weeks. 

I have now worked out the numbers on that assumption and, if my calculations are correct, if you end quarantine at 31 weeks, deaths in the next week due to Covid should be one or zero.]

This analysis assumes that we can control the rate of infection in the younger than seventy population, probably by varying the strength of the sort of restrictions that have been used — limits on large meetings, restaurant seating, and the like. 

What about the cost of older people quarantining? Currently, about 30 million people are seventy or over. Almost all of them are retired, so quarantining does not reduce their income. It does increase some costs, and it makes life substantially less pleasant. Figure pecuniary cost, mostly the cost of having groceries delivered instead of shopping for them, of $10/week. Assume ten percent of the people are not retired and so require an income subsidy of $20,000/year. Run the program for a full year, to allow enough time after herd immunity is reached for the infection to almost disappear, and the total monetary cost is about $76 billion

Final conclusion, based on lots of very uncertain assumptions — this is a back-of-the-envelope calculation:

Cost in lives: 85,000

Cost in money: $76 billion

Time until we can go back to normal for everyone: 1 year or until mass vaccination, whichever is shorter.

Compare that to the current policy. The U.S. death rate is about 5000/week, so it will take 17 weeks of it to kill 85,000 people. Nobody, with the possible exception of President Trump, believes that we will have mass vaccination that soon. So on these figures the herd immunity costs fewer lives, fewer dollars — current subsidies have been measured in trillions — and much fewer restriction.

It does not follow that we should do it, because there is a lot of uncertainty in my calculations. I am accepting John Ioannidis' calculations for mortality, which are controversial. I am ignoring costs such as the problem of separately housing elderly people and younger people who currently live with them. I'm using beds as the relevant measure of hospital capacity, rather than medical personnel. I am assuming that there is no way of substantially expanding ICU capacity, even with considerable excess capacity in non-ICU beds. I am using hospitalization and ICU figures based on current experience, although that experience is heavily weighted towards older patients likely to have more serious cases. I am ignoring tweaks to improve the program, such as identifying the most at risk people under seventy and having them quarantine too, thus bringing down the mortality rate of those not quarantining.

My conclusion is not that we should do it — I don't know enough. It is that the proposal is not absurd, might be an improvement.

Throughout my calculations I have assumed that the quarantining of the elderly is perfectly successful, which is unlikely. My model is for the government to encourage and subsidize self quarantining, not require it — any elderly people who want to risk infection, with a probability of death if infected at about 5%,  are free to do so, and some will. In the worse possible case, where all of the elderly choose to break quarantine and all of them get infected, that would be an additional 1.5 million deaths. [Correction — that was using the case mortality ratio rather than the infection mortality ratio. If I assume the same ratio of cases to infection I have been using, which is probably wrong for the older population, the figure drops to 150,000 deaths. I'm not sure where between those numbers is realistic.] How many it actually will be will depend on how many choose to break quarantine and how many of those get infected.

One more question. Suppose we had followed this policy from the beginning. Using the same assumptions, I get:

Total deaths: 139,000

Time to herd immunity: about a year and a half — or until mass vaccination, whichever is shorter.

Monetary cost: $120 billion, assuming no mass vaccination.

Under our current policy, total deaths are 219,000 so far, likely to run to something close to 400,000 by the time we have mass vaccination. Total monetary cost is hard to estimate but at least an order of magnitude bigger. Total non-monetary human cost probably much larger as well.

Wednesday, October 14, 2020

Cryptography vs. Big Brother: How Math Became a Weapon Against Tyranny

Reason has now run the first two of four episodes in a video about encryption, the Cypherpunks, and related issues. So far they are very good, and I thought people reading this blog might find them of interest.

Part one:

Part two YouTube link:

Facebook link:



Tuesday, October 13, 2020

My First Political Donation?

 Probably not, but I can't remember any others. 

The Arkansas senate contest is a two person race between the Republican incumbent and the Libertarian candidate, the Democratic candidate having for some reason dropped out. Judging by his web page, the Libertarian candidate, Ricky Dale Harrington, is in favor of things all or most of which I am in favor of — and he is polling at 38%. I don't think he is likely to win but it isn't impossible, and a senate with 49 Republicans and one Libertarian plus a Republican VP to break ties, or 50 and 1 plus a Democratic VP, is a tempting vision, possibly the best even marginally plausible outcome I can imagine for this election.

Friday, October 09, 2020

Can Anyone Do Arithmetic?

My current minor irritation is Gavin Newsom, governor of California. He keeps saying things that imply that California needs to reduce its CO2 output in order to reduce global warming in order to prevent future forest fires.

I think it dubious that warming, about a degree C in the U.S. (I don't have figures for California) over the past century plus, has anything to do with the forest fires, but put that aside. Total global warming since it started c. 1913 has been about 1.4°C. The IPCC believes the rate has increased — suppose it is now three degrees a century. The population of California is about 1/200th of the world population, the GNP about 1/40th of the world GNP. I don't have data on CO2, so will guess it is 1/50th of world CO2 output. If California cuts that in half, it reduces world CO2 output by about 1%. Over a century, that might reduce warming by something like .03°c. All calculations are back of the envelope approximations and I know that not all functions in the world are linear, but that's enough to give us some idea of the scale of the effect.

Actually, I'm not so much irritated at Newsom — I expect politicians to be demagogues. I'm irritated at the rest of the world, all of the media and all of the people who take blatant nonsense seriously either because it is says what they want to hear or because they cannot be bothered to do arithmetic.

Trump is a demagogue too, but at least people call him on it.

Sunday, October 04, 2020

Free Audiobooks. Sort of. makes available vouchers for free audiobooks as part of the promotion process. I have such vouchers for The Machinery of Freedom and Future Imperfect.  I will give them to anyone willing to listen to a book and agree that, if he likes it, he will put a favorable review up somewhere that others can see it — a blog, Facebook, Amazon, ...  . 

I have vouchers for both the UK and the US marketplace. If you are interested, give me  contact information either here, via my email, or via FB.

Saturday, October 03, 2020

The Real Problem with Voting by Mail

There has been lots of talk on mail-in voting, with Trump complaining about the possibilities of fraud. The real risk, it seems to me, is not fraud but vote buying. Someone with experience in black markets could offer to buy ballots for ten or twenty dollars apiece, and there are probably places where a fair number of people would sell. 

It would also be possible, but I think more difficult, for someone in a position to pressure many other people, such as an employer, a landlord, perhaps a priest, to give him their ballots to fill out on their behalf or to have everyone fill them out together. That would be more risky, because any one person who complained to the authorities could get him in trouble.

Rothbard, Reagan, and Rand

I recently wrote a chapter on Murray Rothbard for a section on libertarianism in a book I am working on. My central argument was that, because he viewed political conflict as a war between good and evil rather than a conversation among people about their differing beliefs, he was more interested in whether an argument reached the correct conclusion than whether it was true: All is fair in love and war. My first example was an exchange we had during a talk he gave. I wrote that that survived only in my memory, then went on to give other examples from his published work. 

I was wrong. Yesterday I downloaded from the Mises Institute the complete files of the Libertarian Forum, a magazine that Rothbard edited, initially with Karl Hess, from 1969 to 1984. After reading the article I was looking for, one by Rothbard relevant to a different chapter, I did a search on my name and found, among other things, an article by Rothbard clearly written after our exchange. In it he made precisely the same (bad) argument he had made in the talk, added that I and several other people had objected to it, and gave his defense.

The article is  “Are We Being Beastly to the Gipper? Part I," Libertarian Forum XVI Number 1, February 1982. The relevant volume is webbed here. Rothbard's thesis in  it is that, far from cutting government expenditure, Reagan increased it. He wrote:

In fiscal 1980, the last full year of the Carter regime, he of Big Spending and modern liberalism, total federal government spending was $579 billion. Originally, the Reagan projection of his own spending in the first full year of his regime, fiscal 1982, was $695 billion - thus keeping federal spending below the magic $700 billion mark. This "massive" and "historic" spending cut, dear reader, amounted to a 10% annual increase over the budget in the last days of the Bad Old Carter regime.

The problem with this, as should be obvious to any economist, is that these are nominal, not real, figures. From 1980 to 1982, prices increased by about 21%, so the real change implied by those numbers, the change in the quantity of goods and services consumed by government, is not +20% but -1%.

Rothbard went on to point out that the estimate had later increased and was likely to increase even more by the time the year was over. Using the new, higher, estimate for 1982 expenditure, the increase in expenditure was larger than the increase in prices, so his basic conclusion was correct. His argument was not. By using nominal instead of real figures, he had made the increase appear much larger than it actually was.

His response to my pointing that out was that the inflation was Reagan's fault, so it was appropriate to use it to make Reagan look bad. 

The expanded version in the article:

David Friedman, David Henderson, and other "libertarian" apologists for Reaganism have protested that such an attack is unfair since inflation can reduce the "real" level of government spending, as corrected for inflation. But while it is perfectly valid to correct yours and my incomes for inflation to see how well off we really are, it is impermissible to do this for the federal government, which, by its printing of counterfeit money, is itself responsible for the inflation. It is truly bizarre to try to excuse the growth of Reagan spending by pointing to inflation's reducing the "real" level of spending, for in that case, we should hope for an enormous amount of inflation and hail Reagan's spending "reductions" if such hyperinflation came about.  To take a deliberately extreme example to highlight the point: Suppose that the Reagan Administration suddenly doubled the money supply, thereby doubling or tripling the price level next year. Should we then hail Reagan for "cutting" "real" government spending by one-half or two-thirds?

Note the word "unfair" in the second line. The issue was not whether he was being fair to Reagan but whether he was being honest with his audience. Taking his argument seriously, if Reagan doubled the price level we should blame him for inflation, blame him for doubling government expenditure, and praise him for doubling the U.S. economy. I doubt that would have been his response.

Part of what struck me when I found the article was the implication of his publishing it. That implies either that he really believed his own argument, however implausible it seems to me, or that he believed his readers were sufficiently under his spell to accept his arguments, however bad, if given with sufficient confidence and passion.


Which brings me to Ayn Rand. Reading that article and others, I was struck by how similar Rothbard's approach was to Rand's. They disagreed on some issues, most notably anarchism and foreign policy. But they were both arrogantly certain of their positions, argued them with highly emotive language, believed that their natural rights position could be rigorously derived by reason along Aristotelian lines. Both saw political conflict as fundamentally good against evil. Both expected their followers to accept their current line without question.


Early on, Rothbard was an admirer or Rand, joining her circle and writing effusive praise of Atlas Shrugged. That did not last. He left her circle, ceased writing of her with admiration, eventually wrote a one-act play satirizing her and her circle.

There was not enough room for two captains in one boat.


So far as I know, nobody has yet written a book about Rand and Rothbard, their similarities, differences, and interactions. Someone should.